Solve for $x$ and $y$ using elimination. $\begin{align*}-7x+5y &= -8 \\ 7x+3y &= -9\end{align*}$
Solution: We can eliminate $x$ when its corresponding coefficients are negative inverses. Add the top and bottom equations. $8y = -17$ Divide both sides by $8$ and reduce as necessary. $y = -\dfrac{17}{8}$ Substitute $-\dfrac{17}{8}$ for $y$ in the top equation. $-7x+5( -\dfrac{17}{8}) = -8$ $-7x-\dfrac{85}{8} = -8$ $-7x = \dfrac{21}{8}$ $x = -\dfrac{3}{8}$ The solution is $\enspace x = -\dfrac{3}{8}, \enspace y = -\dfrac{17}{8}$.